Build Your Integer Model
Use the grid below to define the objective, bounds, and constraints.
Example Data Table
| Item | Value |
|---|---|
| Objective | Maximize Z = 5x1 + 4x2 + 3x3 |
| Constraint 1 | 2x1 + 3x2 + 1x3 ≤ 17 |
| Constraint 2 | 4x1 + 1x2 + 2x3 ≤ 18 |
| Constraint 3 | 1x1 + 0x2 + 2x3 ≤ 8 |
| Bounds | 0 ≤ x1 ≤ 6, 0 ≤ x2 ≤ 5, 0 ≤ x3 ≤ 4 |
| Optimal solution | x1 = 2, x2 = 3, x3 = 3, Z = 31 |
Formula Used
Integer linear programming seeks the best integer decision vector that satisfies linear constraints.
Maximize or Minimize: Z = c1x1 + c2x2 + ... + cnxn Subject to: a11x1 + a12x2 + ... + a1nxn (<=, >=, =) b1 a21x1 + a22x2 + ... + a2nxn (<=, >=, =) b2 ... am1x1 + am2x2 + ... + amnxn (<=, >=, =) bm Bounds: Li <= xi <= Ui xi are integers
Objective value: The calculator multiplies each decision variable by its objective coefficient and sums the products.
Feasibility test: Every candidate point must satisfy all chosen inequalities or equalities.
Search method: The page enumerates all integer values within the stated bounds, then returns the best feasible objective value.
How to Use This Calculator
- Select maximize or minimize.
- Choose the number of variables and constraints.
- Enter objective coefficients for each variable.
- Set integer lower and upper bounds.
- Fill each constraint coefficient, operator, and right side.
- Press Solve Integer Model.
- Review the optimal solution, feasibility table, and top solutions.
- Download the result as CSV or PDF when needed.
Frequently Asked Questions
1) What does this solver calculate?
It finds the best integer-valued solution for a linear objective under linear constraints and user-defined variable bounds.
2) Does it support minimization and maximization?
Yes. Choose the optimization mode first, then enter the same model data. The solver evaluates the objective accordingly.
3) Are decision variables forced to be integers?
Yes. The search only checks integer values between each variable's lower and upper bounds.
4) Why can large bounds slow the calculation?
The page tests bounded combinations directly. Wider bounds create many more candidate points, so solving takes longer.
5) What happens if no feasible solution exists?
The result area reports that no feasible integer point satisfied all constraints within the selected bounds.
6) Can I use equality constraints?
Yes. Each constraint can use less than or equal, greater than or equal, or exact equality.
7) What does the constraint report show?
It shows the left side value, operator, right side value, and slack, surplus, or gap for the optimal point.
8) What is the Plotly graph displaying?
It compares optimal variable levels and objective contributions, helping you interpret how each decision variable affects the solution.